FIG. 7 is a structural diagram of a conventional interference measuring apparatus 70 used to measure the surface shape of a detected surface 72.
In this interference measuring apparatus 70, light that is emitted from a light source 71 is conducted to both the detected surface 72 and a reference surface 73, and detected light 72a that is generated by the reflection of this light from the detected surface 72 and reference light 73a that is generated by the reflection of this light from the reference surface 73 interfere with each other, so that interference fringes are generated; these interference fringes are then detected by an imaging element 76 such as a CCD imaging element. The two-dimensional distribution of the phase difference between the detected light 72a and reference light 73a can be ascertained from the interference fringes that are thus detected, and the surface shape of the detected surface 72 (using the reference surface 73 as a standard) is expressed by this two-dimensional distribution.
In cases where an even greater increase in precision is desired, the fringe scanning interference method described below is employed.
In this fringe scanning interference method, the reference surface 73 is moved by an amount equal to approximately ½ wavelength by means of a moving mechanism 77 such as a piezo-electric element, so that the optical distance between the detected light 72a and reference light 73a is varied (fringe scan) by an amount equal to approximately one wavelength (one period in terms of the phase difference), and the value of the phase difference (initial phase difference) between the detected light 72a and reference light 73a in a specified state (e.g., the initial state at the time that the fringe scan is initiated) is accurately determined by detecting the variation in the optical density of the interference fringes in this case. Furthermore, the same result can also be obtained by moving the detected surface 72 by an amount equal to approximately ½ wavelength.
Generally, the interference measuring apparatus 70 is set so that the position of the reference surface 73 varies linearly with respect to time during this fringe scan (this is accomplished by the setting of the moving mechanism 77 and a control circuit 78).
Furthermore, in the imaging element 76, charges with quantities that correspond to the intensity of the incident light are accumulated for each unit time Tc in the respective pixels disposed on the light-receiving surface, and the values of the incident light intensity integrated over this time Tc, i.e., the cumulative data B0, B1, B2, . . . are successively output. These cumulative data B0, B1, B2, . . . are used as interference signals.
Assuming that the initial phase difference between the detected light 72a and reference light 73a at a certain point A of the interference fringes is φ0, then, if the amount of variation in the phase difference per unit time Tc, is set equal to 2πa (a constant), the phase difference φ(t) between the detected light 72a and reference light 73a at the point in time where time t has elapsed from the initiation of the fringe scan can be expressed by Equation (1).                               ϕ          ⁡                      (            t            )                          =                                                            2                ⁢                π                ⁢                                                                   ⁢                a                                            T                c                                      ⁢            t                    +                      ϕ            0                                              (        1        )            
Furthermore, the intensity I(t) of the interference light generated by the detected light 72a and reference light 73a can be expressed by Equation (2) using this phase difference φ(t). Moreover, I0 and γ are respective numbers (constants) that are determined by the intensity (amplitude) of the light emitted from the light source 71, etc.I(t)=I0[1+γ cos (φ(t))]  (2)
Furthermore, the relationship between the intensity I(t) of the interference light and the cumulative data B0, B1, B2, . . . constituting the time-integrated values of the interference light intensity over the time Tc can be expressed by Equation (3).                               B          k                =                              ∫                                                            (                                                            2                      ⁢                      k                                        -                    1                                    )                                2                            ⁢                              T                c                                                                                      (                                                            2                      ⁢                      k                                        +                    1                                    )                                2                            ⁢                              T                c                                              ⁢                                    I              ⁢                                                           (              t              )                        ⁢                          ⅆ              t                                                          (        3        )            
Accordingly, the respective cumulative data B0, B1, B2, . . . can be expressed by Equation (4).                               B          k                =                                            I              0                        ⁢                          T              c                                +                                                                      I                  0                                ⁢                γ                ⁢                                                                   ⁢                                  T                  c                                                            π                ⁢                                                                   ⁢                a                                      ⁢            sin            ⁢                                                   ⁢            π            ⁢                                                   ⁢            a            ⁢                                                   ⁢                          cos              ⁡                              (                                                      2                    ⁢                    π                    ⁢                                                                                   ⁢                    a                    ⁢                                                                                   ⁢                    k                                    +                                      ϕ                    0                                                  )                                                                        (        4        )            
If this Equation (4) is transformed, Equation (5) and Equation (6) are obtained.                                                                         B                k                            =                            ⁢                                                                    I                    0                                    ⁢                                      T                    c                                                  +                                                                                                    I                        0                                            ⁢                      γ                      ⁢                                                                                           ⁢                                              T                        c                                                                                    π                      ⁢                                                                                           ⁢                      a                                                        ⁢                  sin                  ⁢                                                                           ⁢                  π                  ⁢                                                                           ⁢                  a                  ⁢                                                                           ⁢                  cos                  ⁢                                                                           ⁢                  2                  ⁢                  π                  ⁢                                                                           ⁢                  a                  ⁢                                                                           ⁢                  k                  ⁢                                                                           ⁢                  cos                  ⁢                                                                           ⁢                                      ϕ                    0                                                  -                                                                                                      ⁢                                                                                          I                      0                                        ⁢                    γ                    ⁢                                                                                   ⁢                                          T                      c                                                                            π                    ⁢                                                                                   ⁢                    a                                                  ⁢                sin                ⁢                                                                   ⁢                π                ⁢                                                                   ⁢                a                ⁢                                                                   ⁢                sin                ⁢                                                                   ⁢                2                ⁢                π                ⁢                                                                   ⁢                a                ⁢                                                                   ⁢                k                ⁢                                                                   ⁢                sin                ⁢                                                                   ⁢                                  ϕ                  0                                                                                                        =                            ⁢                              D                +                                                      X                    k                                    ·                  C                                -                                                      Y                    k                                    ·                  S                                                                                        (        5        )                                                                                                      ∵                  D                                =                                                      I                    0                                    ⁢                                      T                    c                                                              ,                              C                =                                                      I                    0                                    ⁢                  γ                  ⁢                                                                           ⁢                                      T                    c                                    ⁢                  cos                  ⁢                                                                           ⁢                                      ϕ                    0                                                              ,                              S                =                                                      I                    0                                    ⁢                  γ                  ⁢                                                                           ⁢                                      T                    c                                    ⁢                  sin                  ⁢                                                                           ⁢                                      ϕ                    0                                                                                                                                                            X                  k                                =                                                      1                                          π                      ⁢                                                                                           ⁢                      a                                                        ⁢                  sin                  ⁢                                                                           ⁢                  π                  ⁢                                                                           ⁢                  a                  ⁢                                                                           ⁢                  cos                  ⁢                                                                           ⁢                  2                  ⁢                  π                  ⁢                                                                           ⁢                  a                  ⁢                                                                           ⁢                  k                                            ,                                                Y                  k                                =                                                      1                                          π                      ⁢                                                                                           ⁢                      a                                                        ⁢                  sin                  ⁢                                                                           ⁢                  π                  ⁢                                                                           ⁢                  a                  ⁢                                                                           ⁢                  sin                  ⁢                                                                           ⁢                  2                  ⁢                  π                  ⁢                                                                           ⁢                  a                  ⁢                                                                           ⁢                  k                                                                                                      φ0=tan−1 (S/C)  (6)
Furthermore, Equation (7), in which the amount of variation 2πa in the phase difference per unit time Tc is expressed in terms of the four cumulative data B0, B1, B3 and B4, is derived from the above Equation (4).                               2          ⁢          π          ⁢                                           ⁢          a                =                              cos                          -              1                                ⁡                      (                                          1                2                            ⁢                                                                    B                    4                                    -                                      B                    0                                                                                        B                    3                                    -                                      B                    1                                                                        )                                              (        7        )            
On the basis of these relationships, the calculating circuit 79 of the interference measuring apparatus 70 determines the value of a by applying Equation (7) to the respective cumulative data B0, B1, B2, . . . (actually measured values) output by the imaging element 76, and further determines the value of the initial phase difference φ0 from the determined value of a and Equations (5) and (6).
Furthermore, the calculation of the value of this initial phase difference φ0 is respectively performed for the output of each pixel of the imaging element 76, and the two-dimensional distribution of the initial phase difference φ0 thus calculated is output to a display device (not shown in the figures) such as a monitor as shape information for the detected surface 72 using the reference surface 73 as a standard.
Here, in such a fringe scanning interference method, the calculations can be simplified by limiting the manner of movement of the reference surface 73.
For example, if the amount of variation 2πa in the phase difference between the detected light 72a and reference light 73a per unit time Tc is set so that this amount of variation is π/2 (i.e., so that a=¼) as shown in FIG. 8(a), then the initial phase difference φ0 can be directly determined from four consecutive cumulative data, e.g., B0, B1, B2 and B3 (actually measured values), or five consecutive cumulative data, e.g., B0, B1, B2, B3 and B4 (actually measured values), by means of the following Equation (8a) or (8b) (both of these equations are equations derived by setting a so that a=¼ in Equation (4)) (see FIGS. 8(b) and 8(c)):                               ϕ          0                =                              tan                          -              1                                ⁡                      (                                                            B                  0                                -                                  B                  2                                                                              B                  1                                -                                  B                  3                                                      )                                              (8a)                                          ϕ          0                =                              tan                          -              1                                (                                                                                          B                    0                                    +                                      B                    4                                                  2                            -                              B                2                                                                    B                1                            -                              B                3                                              )                                    (8b)            
Furthermore, the method in which the initial phase difference φ0 is determined by means of Equation (8a) from four cumulative data is called the “4-bucket method,” and the method in which the initial phase difference φ0 is determined by means of Equation (8b) from five cumulative data (in this case, the fringe scan is performed for a period of at least (1+¼) in terms of the phase difference) is called the “5-bucket method.” The 5-bucket method requires a longer processing time than the 4-bucket method, since the number of cumulative data on which the method is based is greater by 1; however, the precision is correspondingly higher.
In the respective cumulative data B0, B1, B2, . . . (actually measured values) output by the imaging element 76, a coherent noise component (caused by interference light constituted by noise light that is incident on the imaging element 76 due to excess reflection) is superimposed in addition to the required signal component (based on interference light constituted by the reference light 73a and detected light 72a).
Here, as is indicated by the fine lines in FIG. 7, the noise light consists of noise light that is a part of the light emitted from the light source 71, and that is reflected from some location inside the interferometer 75 so that this light interferes with the detected light 72a or reference light 73a without passing by way of the detected surface 72 or reference surface 73 (noise light b (N)), and noise light that is a part of the light reflected from the detected surface 72 or reference surface 73, and that is reflected by the surfaces of the interference optical system 74 or the emission port of the light source 71, etc., so that this light again travels toward the detected surface 72 or reference surface 73, and interferes with the detected light 72a or reference light 73a after being reflected by the detected surface 72 or reference surface 73 (noise light c (WNW), noise light d (WNR), noise light e (RNR) and noise light f (RNW)).
Furthermore, the alphabetic characters in parentheses indicate the reflection path. Specifically, the reflection path of the detected surface 72 is indicated by W, the reflection path of the reference surface 73 is indicated by R, and the reflection path of any location inside the interferometer 75 is indicated by N (since the reflectivity of any location inside the interferometer 75 is sufficiently smaller than the reflectivity of the detected surface 72 or reference surface 73, noise light that has been reflected two or more times at such a location can be ignored).
It is desirable that the coherent noise components that are superimposed on the interference signals by such noise light b, c, d, e and f be separated from the required signal components and eliminated by some type of operation.
However, in the case of a conventional interference measuring apparatus 70, as is also clear from the application of the above-mentioned Equations (8a) and (8b), it is considered that coherent noise components are not superimposed on the cumulative data B0, B1, B2, . . . (actually measured values); accordingly, the initial phase difference φ0 that is finally determined as the shape information contains error.
Here, in the case of coherent noise components that vary with a different period than that of the required signal components, these noise components can be separated from these signal components by some type of operation; however, coherent noise components that vary with the same period as that of the required signal components cannot be separated even if some type of operation is applied.
Incidentally, among the coherent noise components occurring in the interference measuring apparatus 70, the component generated by the interference of the noise light b with the reference light 73a, the component generated by the interference of the noise light c with the reference light 73a, the component generated by the interference of the noise light d with the detected light 72a, the component generated by the interference of the noise light e with the reference light 73a and the component generated by the interference of the noise light f with the reference light 73a vary with the same period as that of the required signal components as the reference surface 73 moves; accordingly, separation (i.e., elimination) of these noise components is impossible (details will be described later; see Table 2).
It is conceivable that the generation itself of the noise light b, c, d, e and f causing the coherent noise components might be avoided by altering the optical elements inside the interferometer 75; however, since noise light generated in accordance with the reflectivity values and disposition angles of the surfaces of the optical elements may be generated to a considerable extent regardless of the optical elements that make up the interferometer, complete avoidance is impossible.
Conventionally, therefore, suppression of the effects of coherent noise components has been viewed as impossible, whether by altering the contents of the calculations or altering the hardware, and all that has been done is to accomplish a slight suppression of the intensity of coherent noise components by forming anti-reflection films on the surfaces of the optical elements, or inserting elements for the purpose of removing excess reflected light from the light path.